.Let be the function given by for .
a) Calculate the fourier coefficients of and show that...
b) What is the Fourier series of in terms of sines and cosines?
My answer, .
For even n's the summands of this series are zero, so you can take only odd n's in the sum and since you have a square in the denominator this
is the same as twice the sum over the odd natural numbers (taking ):
Now equal the above to zero and you'll get what you want...
c) Taking , prove that
Now this, I suspect, should have just been a simple application of Parsevals theorem but I'm going wrong somewhere.
But with the left hand side is 0.
Thus we get,
So clearly I'm doing something wrong... Most likely in that last 2 steps...